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Factorization Of Polynomials [NEW] — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Polynomials [NEW]5 Marks
Question
The expression x4 + 4 can be factorized as:
  1. (x2 + 2x + 2)(x2 - 2x + 2)
  2. (x2 + 2x + 2)(x2 + 2x - 2)
  3. (x2 - 2x - 2)(x2 - 2x + 2)
  4. (x2 + 2)(x2 - 2)
✓

Answer

  1. (x2 + 2x + 2)(x2 - 2x + 2)

Solution:

x4 + 4

= x4 + 4 + 4x2 - 4x2

= (x4 + 4x2 + 4) - 4x2

= (x2 + 2)2 - (2x)2

= (x2 + 2 - 2x)(x2 + 2 + 2x)

= (x2 + 2x + 2)(x2 - 2x + 2)

Hence, correct option is (a).

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